What is taylor x^2e^{x^2} ?

The answer to taylor x^2e^{x^2} is x^2+x^4+1/2 x^6+1/6 x^8+1/24 x^{10}+\ldots

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taylor x^2e^{x^2}

taylor

x^{2} e^{x^{2}}

x^{2} + x^{4} + \frac{1}{2} x^{6} + \frac{1}{6} x^{8} + \frac{1}{24} x^{10} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( x ^{2} e ^{x^{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{2} e ^{x^{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{2} e ^{x^{2}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{360}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{6720}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{151200}{10 !} x^{10} + \dots

Refine

= x^{2} + x^{4} + \frac{1}{2} x^{6} + \frac{1}{6} x^{8} + \frac{1}{24} x^{10} + \dots

n = 1 \sum \infty n \cdot (\frac{3}{4})^{n}

\int \frac{9 - x ^{2}}{x ^{3}} d x

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What is taylor x^2e^{x^2} ?
The answer to taylor x^2e^{x^2} is x^2+x^4+1/2 x^6+1/6 x^8+1/24 x^{10}+\ldots